(a) No, it won't. The remainder will be the same as that for the number that isn't divisible by n.

(b) It might be, and it might not. Consider whether (8+4) is divisible by 3, given that neither 8 nor 4 is divisible by 3; then consider whether (8+5) is divisible by 3, given that neither 8 nor 5 is divisible by 3.

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